That single most used piece of photography advice available on the internet is garbage. Any photographer who spouts it is an amateur. If the photographer you've hired for family pictures uses it, you might want to rethink hiring them.
Have you ever seen a professional photographer at a wedding without a flash on their camera? That's because they know something those amateurs do not.
Flash lighting exists for a reason and that reason is not every subject comes with perfect lighting. Sometimes you've got back lighting, or overly strong side lighting or just plain not enough lighting. If you have to use a tripod because your shutter speed is that slow, chances are a human being in the photo isn't going to be able to hold still well enough either. That's what flashes and strobes and hot lights are for. They fill in and add enough light so you can take the picture.
This doesn't mean that I think we should all go back to the deer in the headlights straight on flash. What you should do is learn to use it. There are a ton of really great tutorials on the internet about flash photography. Instead of telling yourself flash is evil, do some research. Practice. Figure it out. Your camera flash can be one of your best tools if you know what you are doing with it.
For example, this is my sitting room. This picture was taken without a flash using a tripod. Notice how dark the chairs are. There's no detail because of the high contrast from the back lighting. I could mess with the contrast levels in photoshop and try to come up with something acceptable. But why?
When I could just get my accessory flash and bounce it off the ceiling (with a Lightsphere attached) and get the lighting I need.
Some of you may say you like the first photo. Fine, but you have to admit that when my purpose of taking the photograph is to show the furniture and the room, the first photo doesn't cut it.
I'm not going to tell you I'm a flash expert. I'm definitely not going to claim that all photography on this blog is fabulous. (The vast majority of is is far from not fabulous because I am fabulously lazy.) I will say this: learn to use your flash. Buy accessories for your flash so you can use it to best effect. Then learn some more.
Anytime you lock yourself in the box of "never" doing something with your craft, you lose. Don't say "never." Say, "learn." And for heaven's sake, check someone's credentials, including mine, before you follow their advice.